Computing convolutions by reciprocal search
SCG '86 Proceedings of the second annual symposium on Computational geometry
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
A fast depth-buffer-based voxelization algorithm
Journal of Graphics Tools
Fast swept volume approximation of complex polyhedral models
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
The Minkowski Sum of Two Simple Surfaces Generated by Slope-Monotone Closed Curves
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Computing the Minkowski sum of ruled surfaces
Graphical Models
Robust repair of polygonal models
ACM SIGGRAPH 2004 Papers
Real-time Voxelization for Complex Polygonal Models
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Accurate Minkowski sum approximation of polyhedral models
Graphical Models - Special issue on PG2004
A Simple Algorithm for Complete Motion Planning of Translating Polyhedral Robots
International Journal of Robotics Research
Exact and efficient construction of planar Minkowski sums using the convolution method
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Real-time voxelization of triangle meshes on the GPU
ACM SIGGRAPH 2007 sketches
Minkowski sum boundary surfaces of 3D-objects
Graphical Models
Exact and efficient construction of Minkowski sums of convex polyhedra with applications
Computer-Aided Design
Spatial Planning: A Configuration Space Approach
IEEE Transactions on Computers
Covering Minkowski sum boundary using points with applications
Computer Aided Geometric Design
Algorithmica - Special Issue: European Symposium on Algorithms 2007, Guest Editors: Larse Arge and Emo Welzl
Configuration products in geometric modeling
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Group morphology with convolution algebras
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
GPU-based offset surface computation using point samples
Computer-Aided Design
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We present a new approach for computing the voxelized Minkowski sum (excluding any enclosed voids) of two polyhedral objects using programmable Graphics Processing Units (GPUs). We first cull out surface primitives that will not contribute to the final boundary of the Minkowski sum, analyzing and adaptively bounding the rounding errors of the culling algorithm to solve the floating point error problem. The remaining surface primitives are then rendered to depth textures along six orthogonal directions to generate an initial solid voxelization of the Minkowski sum. Finally we employ fast flood fill to find all the outside voxels. We generate both solid and surface voxelizations of Minkowski sums without enclosed voids and support high volumetric resolution of 1024^3 with low video memory cost. The whole algorithm runs on the GPU and is at least one order of magnitude faster than existing boundary representation (B-rep) based algorithms. It avoids the large number of 3D Boolean operations needed in most existing algorithms and is easy to implement. The voxelized Minkowski sums can be used in a variety of applications including motion planning and penetration depth computation.